As described in Patent Documents 1 and 2, in an automatic transmission for a vehicle, a lock-up clutch capable of mechanically coupling an output shaft of an engine to an input shaft of the automatic transmission is provided in a torque converter. In addition, by engaging the lock-up clutch under certain conditions, engine rotation speed is kept low to improve fuel consumption.
Generally, the lock-up clutch is engaged when the automatic transmission is set to a predetermined gear shift stage. However, shocks and torque fluctuations transmitted between the input shaft and the output shaft cannot be absorbed when the lock-up clutch is fully engaged. Accordingly, depending on driving conditions of the vehicle, slip control is performed to slip the lock-up clutch without being fully engaged. In this slip control, for example, depending on driving conditions, a target slip ratio of the lock-up clutch is recorded corresponding to a gear shift stage, and an engaging capacity of the lock-up clutch is controlled (controlled by feedback control) so that an actual slip ratio can be equivalent to the target slip ratio.